Extend count repated

Hi. I have the following formula: countif($A$1$A:$9,$A$1:$A$9) and id counts the number of repeated cells the the range A1:A9. I need to extend this to work in two or more columns, that is, I want something like this: countif($A$1:$B$9,$A$1:$B$9) (result in C) but it doesn't work. But I need to count as pairs (a, b) and not just for each cell (see the illustration bellow).

A B C
------------
1 | a | b | 2 |
------------
2 | a | c | 1 |
------------
3 | a | b | 2 |
------------

To better understand, please see the attachment.

Thanks in advance,
jacome